And if you do not know the original encoding at all, but you can tell a few characters for sure, this might help:

use strict;
use warnings;

use Encode "decode";
binmode STDOUT, ":utf8";

my @enc = grep { !m/^mime/i } Encode->encodings (":all");
my $c = pack "H*", shift;
foreach my $e (@enc) {
    my $x = eval { decode ($e, $c) };
    !defined $x || $x =~ m/^(?:$|\x{fffd})/ and next;
    printf "  %-30s %s\n", $e, $x;
    }
[download]

If you know that in your text, \xD7 is × and \xE4 is ä, then:

$ find_enc d7e4 | grep ×ä
  cp1250                         ×ä
  cp1252                         ×ä
  cp1254                         ×ä
  cp1257                         ×ä
  cp1258                         ×ä
  iso-8859-1                     ×ä
  iso-8859-13                    ×ä
  iso-8859-15                    ×ä
  iso-8859-2                     ×ä
  iso-8859-3                     ×ä
  iso-8859-4                     ×ä
  iso-8859-9                     ×ä
  UTF-7                          ×ä
$
[download]

The more you know, the smaller your result set might be. If you also know that \xF0 is đ or š, you're down to 4 or even 2:

$ find_enc d7e4f0 | grep ×äđ
  cp1250                         ×äđ
  cp1258                         ×äđ
  iso-8859-2                     ×äđ
  iso-8859-4                     ×äđ
$ find_enc d7e4f0 | grep ×äš
  cp1257                         ×äš
  iso-8859-13                    ×äš
$
[download]